On the advantage of centralized strategies in the three-pursuer single-evader game

Cooperation in multi-pursuer games is known to be useful. However, it is not easy to quantify how much it is convenient for the pursuers to play according to a centralized strategy with respect to a decentralized one. This paper provides an answer to this question, for the problem of three pursuers chasing a single evader in a planar environment. It is shown that centralized pursuit algorithms can halve the time required to capture the evader, with respect to decentralized pursuit strategies. Moreover, this limit is proven to be tight. Numerical computations of lower bounds to the ratio between the capture times of centralized and decentralized strategies, show that for several game initial conditions the benefit of playing in a centralized way may be significantly less than halving the game duration.